37. Identifying the Lighter Coin You have a total of 81 coins. Out of these, 80 coins are white and weigh 5 grams each, while 1 coin is white and weighs 4 grams. What is the minimum number of times you use the scale to determine which coin is the lighter one? Added 29 April 2016 · Updated 8 July 2026 Guess: Guess | Show Solution Solution: 1. Split the 81 coins into three piles of 27 and balance two of the piles. • If they balance, the lighter coin is in the pile left aside. • If not, the lighter side contains it. 2. Take the suspect 27 coins, divide them into three piles of 9 and balance two of them. • The lighter (or unweighed) pile contains the lighter coin. 3. From those 9 coins, make three piles of 3 and balance two of them. • The lighter (or unweighed) pile contains the lighter coin. 4. With the final 3 coins, balance one coin against another. • If one is lighter, it is the 4-gram coin. • If they balance, the coin not on the scale is the lighter one. This locates the single 4-gram coin in exactly four weighings.
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